Naslov
Testing Equality of Distributions of Random Convex Compact Sets via Theory of 𝕹-Distances

Autori
Gotovac Đogaš, Vesna ; Helisová, Kateřina

Izvornik
Methodology and computing in applied probability (1387-5841) 23 (2021), 2; 503-526

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
characteristic function ; non-parametric method ; permutation test ; support function ; two-sample problem

Sažetak
This paper concerns a method of testing the equality of distributions of random convex compact sets. The main theoretical result involves a construction of a metric on the space of distributions of random convex compact sets. We obtain it by using the theory of N - distances and the redefined characteristic function of random convex compact set. We propose an approximation of the metric through its finite- dimensional counterparts. This result leads to a new statistical test for testing the equality of distributions of two random convex compact sets. Consequently, we show a heuristic approach how to determine whether two realisations of random sets that can be approximated by a union of identically distributed random convex compact sets come from the same underlying process using the constructed test. Each procedure is justified by an extensive simulation study and the heuristic method for comparing random sets using their convex compact counterparts is moreover applied to real data concerning histological images of two different types of mammary tissue.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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